New posts in algebraic-topology

Topological groups, why need them?

general-topology algebraic-topology soft-question topological-groups motivation

Can we generalize the regular value theorem even beyond the Ehresmann's theorem?

differential-geometry algebraic-topology manifolds fiber-bundles

different definitions of Hopf algebras

abstract-algebra ring-theory algebraic-topology homology-cohomology hopf-algebras

Visualizing Hopf fibration $S^3\to S^2$ as a based map $S^1\to \mathrm{Map}(S^2,S^2)$

algebraic-topology homotopy-theory fiber-bundles visualization hopf-fibration

Is wedge sum for finite CW complexes cancellative in the homotopy category?

algebraic-topology homotopy-theory cw-complexes

Fundamental group of quotient spaces of $SO(3)$

algebraic-topology

A simply-connected closed surface is a sphere

algebraic-topology surfaces geometric-topology alternative-proof low-dimensional-topology

Can torsion in the fundamental group happen in "the real world"

algebraic-topology cw-complexes

Tautological line bundle over $\mathbb{RP}^n$ isomorphic to normal bundle? Also "splitting" of transition functions

general-topology differential-geometry algebraic-topology manifolds differential-topology

Obstructions to lifting a map for the Hopf fibration

algebraic-topology differential-topology

The fundamental group of a pair of Hawaiian earrings

algebraic-topology

If the top Stiefel-Whitney class of a compact manifold is nonzero, must there be another non-vanishing Stiefel-Whitney class?

algebraic-topology characteristic-classes

Is there a name for this constant associated to smooth maps between spheres? (not degree)

algebraic-topology differential-topology smooth-manifolds homotopy-theory de-rham-cohomology

Modern Research in Algebraic Topology

algebraic-geometry algebraic-topology soft-question

Spine of a noncompact surface with proper retraction

algebraic-topology differential-topology surfaces geometric-topology

What are the best known results for the stable homotopy groups of spheres?

algebraic-topology homotopy-theory

De Rham cohomology of the plane with $m$ holes

algebraic-topology

Is the plane minus the integer lattice homeomorphic to the plane minus the integers?

general-topology algebraic-topology

Can we always view loops as maps from $S^1\to X$?

algebraic-topology fundamental-groups

How to read Hatcher's Algebraic Topology?

algebraic-topology soft-question